What Are the 7 Properties and 4 Types of Parallelograms?
Properties of Parallelograms are essential in geometry for recognising shapes, solving angle and area problems, and preparing for exams like CBSE and Olympiads. Knowing these core features helps you classify quadrilaterals and solve challenging maths questions with confidence. Practice makes perfect!
Formula Used in Properties of Parallelograms
The standard formula is: \( \text{Area} = \text{base} \times \text{height} \) and \( \text{Perimeter} = 2 \times (\text{sum of adjacent sides}) \). The properties also include diagonal bisection and congruent triangles within the parallelogram.
Here’s a helpful table to understand Properties of Parallelograms more clearly:
Properties of Parallelograms Table
| Property | Description | Applies to All Parallelograms? |
|---|---|---|
| Opposite sides equal | Both pairs of opposite sides have the same length. | Yes |
| Opposite sides parallel | Both pairs of opposite sides are parallel. | Yes |
| Opposite angles equal | Both pairs of opposite angles are equal. | Yes |
| Consecutive angles supplementary | Two adjacent angles add up to 180°. | Yes |
| Diagonals bisect each other | Each diagonal cuts the other exactly in half. | Yes |
| Each diagonal forms congruent triangles | Divides into two equal triangles. | Yes |
| Special types (rectangles, rhombuses, etc.) | May have additional properties, e.g. equal diagonals. | No |
This table shows how the pattern of Properties of Parallelograms appears regularly in real cases.
Worked Example – Solving a Problem
1. In parallelogram ABCD, if AB = 5 cm and BC = 8 cm, find the perimeter.Step 2: Substitute the values: Perimeter = 2 × (5 + 8) cm = 2 × 13 cm = 26 cm.
Final Answer: 26 cm
2. In parallelogram PQRS, diagonal PR = 10 cm and PR is bisected at point O. Find PO.
Final Answer: 5 cm
Practice Problems
- List all properties of parallelograms you can recall.
- If one angle of a parallelogram is 70°, what are the other three angles?
- Does a parallelogram always have equal diagonals?
- Find the area if base = 12 cm and height = 5 cm.
- Which shapes from Types of Quadrilaterals are always parallelograms?
Common Mistakes to Avoid
- Confusing properties of parallelograms with those of rectangles or rhombuses.
- Assuming diagonals are always equal (true for rectangles, not all parallelograms).
- Forgetting consecutive angles are supplementary (add up to 180°), not always equal.
- Mixing up parallel with equal—parallel sides must both be equal in a parallelogram.
Real-World Applications
You’ll see properties of parallelograms in engineering, design, and construction—like bridges, tiles, and frames. Understanding these properties lets you solve spatial puzzles and improve pattern recognition. For more on classroom connections, visit Parallelogram Law for vector addition in physics.
Page Summary
We explored the idea of properties of parallelograms, how to apply them, solved related problems, and learned their connection to real-life designs. Practice regularly with Vedantu and try worksheets on Parallelogram, Construction of a Parallelogram, or compare with Difference Between Rhombus and Parallelogram to master this vital geometry topic.
FAQs on Parallelogram Properties: Complete Guide for Students (2025)
1. What are the 7 properties of a parallelogram?
The seven properties of a parallelogram include:
1. Opposite sides are parallel.
2. Opposite sides are equal in length.
3. Opposite angles are equal.
4. The diagonals bisect each other.
5. Each diagonal divides the parallelogram into two congruent triangles.
6. The sum of any two adjacent angles is 180°.
7. Both pairs of opposite sides are congruent and parallel.
These properties are crucial for understanding and solving geometry problems related to parallelograms.
2. What is the property 5 of a parallelogram?
The fifth property of a parallelogram is that each diagonal divides the parallelogram into two congruent triangles. This means the two triangles formed have equal area and corresponding sides and angles are equal.
3. What is a property of all parallelograms?
A key property of all parallelograms is that the opposite sides are both equal in length and parallel. This property is always true for every parallelogram.
4. What are the 4 types of parallelograms?
The four types of parallelograms are:
1. Rectangle – All angles are 90°, opposite sides are equal.
2. Rhombus – All sides are equal and opposite angles are equal.
3. Square – All sides and angles are equal (a special rectangle and rhombus).
4. General parallelogram – Only opposite sides and angles are equal, but sides and angles are not always right angles or all equal.
5. What are the properties of the diagonals of a parallelogram?
The diagonals of a parallelogram have these main properties:
a) They bisect each other (each diagonal divides the other into two equal parts).
b) They do not always have equal length.
c) In special parallelograms such as rectangles and squares, the diagonals are equal.
d) In a rhombus, the diagonals are perpendicular and bisect each other at 90 degrees.
6. What are the properties of a rectangle?
A rectangle has these properties:
1. Opposite sides are equal and parallel.
2. All angles are 90 degrees.
3. The diagonals are equal in length and bisect each other.
4. The sum of the adjacent angles is 180 degrees.
7. What are the properties of a rhombus?
A rhombus has these properties:
1. All sides have equal length.
2. Opposite sides are parallel.
3. Opposite angles are equal.
4. Diagonals bisect each other at 90 degrees (perpendicular).
5. Diagonals bisect the angles of the rhombus.
8. What are the properties of a trapezium?
A trapezium (also known as a trapezoid) has the following properties:
1. Only one pair of opposite sides are parallel.
2. The non-parallel sides are called legs.
3. The angles between a leg and a base are supplementary in an isosceles trapezium.
4. The diagonals may be of equal length in an isosceles trapezium.
9. What are the properties of a kite?
A kite in geometry has these main properties:
1. It has 2 pairs of equal-length adjacent sides.
2. One pair of opposite angles (where the different pairs meet) are equal.
3. The diagonals intersect at right angles (perpendicular).
4. One diagonal bisects the other.
10. What are the properties of parallelograms notes for Class 9?
For Class 9 CBSE, the key properties of a parallelogram you need to remember are:
1. Opposite sides and angles are equal.
2. Opposite sides are parallel.
3. Diagonals bisect each other.
4. Adjacent angles are supplementary.
5. Each diagonal divides the parallelogram into two congruent triangles.
11. How do you find missing angles in a parallelogram?
To find missing angles in a parallelogram:
1. Use the property that opposite angles are equal.
2. Use the property that adjacent angles are supplementary (add up to 180 degrees).
3. Set up an equation with the given values and solve accordingly.
12. What are the 6 properties of a parallelogram?
The six main properties of a parallelogram are:
1. Opposite sides are equal and parallel.
2. Opposite angles are equal.
3. Diagonals bisect each other.
4. Adjacent angles are supplementary.
5. Each diagonal divides the parallelogram into two congruent triangles.
6. The area formula is base × height.
